EP3640602B1 - Verfahren zum nachweis von fehlern in einem drehpositionssensorsystem mit sinus- und kosinus-signalen - Google Patents

Verfahren zum nachweis von fehlern in einem drehpositionssensorsystem mit sinus- und kosinus-signalen Download PDF

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EP3640602B1
EP3640602B1 EP19203287.8A EP19203287A EP3640602B1 EP 3640602 B1 EP3640602 B1 EP 3640602B1 EP 19203287 A EP19203287 A EP 19203287A EP 3640602 B1 EP3640602 B1 EP 3640602B1
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sine
cosine
data
signal
offset
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EP3640602A1 (de
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Josef Janisch
Erhard Müsch
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Renesas Electronics America Inc
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Integrated Device Technology Inc
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01D—MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
    • G01D5/00—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable
    • G01D5/12—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable using electric or magnetic means
    • G01D5/14—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable using electric or magnetic means influencing the magnitude of a current or voltage
    • G01D5/20—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable using electric or magnetic means influencing the magnitude of a current or voltage by varying inductance, e.g. by a movable armature
    • G01D5/204—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable using electric or magnetic means influencing the magnitude of a current or voltage by varying inductance, e.g. by a movable armature by influencing the mutual induction between two or more coils
    • G01D5/2053—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable using electric or magnetic means influencing the magnitude of a current or voltage by varying inductance, e.g. by a movable armature by influencing the mutual induction between two or more coils by a movable non-ferromagnetic conductive element
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01D—MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
    • G01D5/00—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable
    • G01D5/12—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable using electric or magnetic means
    • G01D5/244—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable using electric or magnetic means influencing characteristics of pulses or pulse trains; generating pulses or pulse trains
    • G01D5/24471—Error correction
    • G01D5/2448—Correction of gain, threshold, offset or phase control
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01D—MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
    • G01D3/00—Indicating or recording apparatus with provision for the special purposes referred to in the subgroups
    • G01D3/028—Indicating or recording apparatus with provision for the special purposes referred to in the subgroups mitigating undesired influences, e.g. temperature, pressure
    • G01D3/036—Indicating or recording apparatus with provision for the special purposes referred to in the subgroups mitigating undesired influences, e.g. temperature, pressure on measuring arrangements themselves

Definitions

  • Embodiments of the present invention are related to position sensors and, in particular, to a method for detecting errors in a rotational position sensor system having sine and cosine signals.
  • Position sensors are used in various settings for measuring the position of one component with respect to another.
  • Inductive position sensors can be used in automotive, industrial and consumer applications for absolute rotary and linear motion sensing.
  • a transmitter coil is driven to induce eddy currents in a metallic target that is sliding or rotating above a set of receiver coils.
  • Receiver coils receive the magnetic field generated from eddy currents and the transmitter coils and provide signals to a processor.
  • the processor uses the signals from the receiver coils to determine the position of the metallic target above the set of receiver coils.
  • the processor, transmitter coils, and receiver coils may all be formed on a printed circuit board (PCB).
  • PCB printed circuit board
  • Another effective way is to use a redundant method where two independent sensors are measuring the same physical parameter (e.g. rotary position) and the Electric Control Unit (ECU) compares the two sensor results.
  • ECU Electric Control Unit
  • the sensor signal cannot be interrupted during operation, therefore it is not allowed, for example, to replace the sensor raw signal with a known reference signal for making a reference measurement. Therefore, the error analysis must be performed with the un-interrupted sine and cosine signals.
  • JP 2017 151061 A US 2014/331076 A1 , EP 1 341 311 A2 or JP 2010 071783 A .
  • a method of correcting for errors in a rotational position sensor having a sine signal and a cosine signal includes compiling data from the sine signal and the cosine signal over a period of rotation of a motor shaft; determining offset correction parameters from the data; correcting the data with the offset correction parameters; determining amplitude difference parameters from the data; correcting the data with the amplitude difference parameters; determining phase difference parameters from the data; correcting the data with the phase difference parameters; and using the offset correction parameters, the amplitude difference parameters, and the phase difference parameters to correct the sine signal and the cosine signal.
  • position sensors particularly position sensors for detecting rotary movement, provide the raw sensor data in the form of sinusoidal signal, where one period of the sensor signal may represent a full turn or fractions of a full turn of the item being measured (e.g. a rotor in an electric motor).
  • a second signal is introduced, which is again sinusoidal in format, but phase shifted by a quarter of one phase, or 90 electrical degrees. While the first signal is typically designated as Sine-signal, the second signal is typically designated as Cosine signal.
  • Such types of position sensor include, but are not limited to magnetic sensors, such as Hall, AMR (anisotropic magneto resistance), TMR (tunneling magneto resistance) or GMR (giant magneto resistance) sensors as well as inductive or eddy current sensors.
  • magnetic sensors such as Hall, AMR (anisotropic magneto resistance), TMR (tunneling magneto resistance) or GMR (giant magneto resistance) sensors as well as inductive or eddy current sensors.
  • FIG. 1A illustrates a block diagram of a position sensor 100.
  • position sensor 100 includes a transmitter coil 104 and receiver coils 106 coupled to a controller 102.
  • Controller 102 drives transmitter coil 104 to generate a time-varying magnetic field, which induces eddy currents in a conductive target that is in a position relative to transmitter coil 104 and receiver coils 106.
  • Receiver coils 106 are positioned within transmitter coil 104 and provides a signal related to the spatial superposition of magnetic fields generated by the transmitter coil and the magnetic fields generated by the eddy currents induced in the conductive target positioned over the receiver coils 106.
  • transmitter coil 104 and receiver coils 106 can be arranged to provide sensors of varying geometry, including linear and rotational positioning.
  • Figures 1B and 1C illustrate a planar view and a cross-sectional view of a rotational inductive position sensor.
  • Figure 1B illustrates position sensor coils 110.
  • Position sensors coils 110 includes transmitter coil 104 and receiver coils 106 formed on a printed circuit board 112. As is illustrated in Figure 1B , position sensor coils 110 are formed in a circular fashion.
  • Transmitter coil 104 is formed in a circle around receiver coils 106.
  • Receiver coils 106 can typically be two coils, a sine-coil that generates a sine signal as a target is rotated over receivercoils 106 and a cosine-coil that generates a cosine signal as the target is rotated over receiver coils 106.
  • Leads 118 provide electrical connections between transmitter coil 104 and receiver coils 106 and controller 102 as illustrated in Figure 1A .
  • Figure 1C further illustrates operation of position sensor 100 using position sensor coils 110. As shown in Figure 1C , transmitter coils 104 and receiver coils 106 are formed on PCB 112.
  • Transmitter coils 104 and receiver coils 106 can be formed on both sides of PCB 112.
  • a circular hole 108 is formed in the center of position sensor coils 110 through which a rotor shaft 114 can pass.
  • a target 116 which is positioned to rotate over receiver coils 106, is coupled to rotor shaft 114.
  • FIG 2A illustrates a graph of raw output signals from a position sensor 100 as illustrated in Figures 1A, 1B, and 1C .
  • receiver coils 106 include a sine coil and a cosine coil.
  • the horizontal axis of the graph represents the mechanical rotation (in this case 0-360 degrees)
  • the vertical axis of the graph shows the output voltages from the sine coil and the cosine coil of receiver coils 106.
  • the amplitude of the cosine signal B is slightly larger than the amplitude of the sine signal A.
  • the angle ⁇ can be designated in degrees or radians.
  • Position arctan a sin * sin x a cos * cos x ⁇
  • Position arctan sin x cos x in radians
  • Position arctan a sin * sin ⁇ a cos * cos ⁇ ⁇ 180 ⁇ ⁇
  • Position arctan sin ⁇ cos ⁇ ⁇ 180 ⁇ in degrees
  • Figure 2B illustrates another depiction, a polar coordinate system, of the sine and cosine output signals from receiver coils 106.
  • a and B are representative of the signal level strength.
  • the X-axis is represented by the cosine signal V cos and the Y-axis is represented by the sine signal V sin .
  • the value ⁇ in this graph depicts the angular vector of the signal, which is the rotational position of target 116 to be measured.
  • the Magnitude (“MAG”) is the length of the vector, the peak level of the signals.
  • the polar representation of such signals is a perfect circle, centered around the zero position, at the crossing of the X and Y axis.
  • Peak amplitude A for sine and A for the cosine signal is assumed to be 1 in the graphical representation depicted in the ideal situation illustrated in Figure 2B .
  • the magnitude vector has a constant length across the full circle, and the positional error (i.e., the difference between the calculated position of the target and its actual position) over the full 360° range is zero.
  • Figure 2C illustrates the sine and cosine signals for an error free set of coordinates with magnitude 1.
  • Figure 2C illustrates the ideal situation where the sine signal 202 represented as V sin ( ⁇ ) and the cosine signal 204 represented by V cos ( ⁇ ) with a resulting signal magnitude (MAG) 206 of 1 through all angles. This results in a full-scale (FS) percent error 208 of 0 through all angles.
  • FS full-scale
  • the signal path may contain errors. These can be categorized into (1) Offset errors: one or both signals are shifted in the voltage domain in either the positive or negative direction; (2) Gain mismatch errors: different gains of sine and cosine signal path resulting in a mismatch of the amplitudes; and (3) Phase errors resulting in a phase shift between sine signal and cosine signal that is not 90°. In a system having such errors, the magnitude vector length is no longer a constant value throughout one period. However, as is further illustrated below, these errors represent distinctive patterns over one period, based on the type of error.
  • Embodiments of the present invention analyze the pattern of the magnitude vector length within a minimum of half a period of rotation, ideally one full period of rotation, and provides evidence about the type of errors and the size of the error in that system. This data can be used to correct the processing so that more accurate positional determinations can be made.
  • the input signals are constantly monitored and the angular position is calculated using the arctangent of the ratio of the sine and cosine signals as described above. In some embodiments, other appropriate methods, such as a look-up table, can be used. Likewise, the Magnitude of the signals using the square root of the square sum of sine and cosine signals, as described earlier is calculated. By monitoring the minimum and maximum signal levels (peak-to-peak magnitude) as well as the number of periods of that signal within one electrical period, the type of error along with the strength of that error can be estimated by the methods described further in this document.
  • MAG is the magnitude of a signal including offset, amplitude mismatch and phase errors, such as that depicted in the polar coordinate system illustrated in Figure 2B .
  • ⁇ sin is the offset level on the sine signal
  • ⁇ cos is the offset level on the cosine signal
  • a sin is the amplitude level of the sine signal
  • a cos is the amplitude of the cosine signal
  • ⁇ is the angular position (0° ⁇ 360°)
  • ⁇ is the phase error (difference from 90°) of the cosine signal relative to the sine signal.
  • Figure 3 shows a signal path diagram for system 100.
  • the sine signal and the cosine signal from position sensor receiver coils 106 is input to an analog circuit 320 and then to a digital electric control unit (ECU) 322. Consequently, the raw sine and cosine signals from the position sensor receiver coils 106 is amplified, rectified, and filtered in analog section 320 before being sent to the receiving electrical control unit 322, where the signals are converted to the digital domain and further processed.
  • the sine signal is input to an offset adder 302 where an AC offset voltage is added.
  • the signal from offset adder 302 is then amplified in amplifier 306, rectified in rectifier 324, and filtered in filter 310.
  • the cosine signal is input to an offset adder 304 where an offset voltage is added, an amplifier 308 that amplifies the signal, a rectifier 326, and a filter 312 that filters the signal.
  • Rectifiers 324 and 326 rectify the signals from amplifiers 306 and 308, respectively, and output signals with DC average values proportional (x 2/ ⁇ ) to the amplitudes of the amplified sign and cosine receiver voltages, respectively.
  • the remaining high frequency component of the signals is removed by filters 310 and 312, respectively.
  • the amplified and filtered sine signal and cosine signal are then input to ECU 322.
  • the sine signal is digitized in analog-to-digital converter (ADC) 314 to obtain a digitized signal V sin and input to digital signal processing 318.
  • ADC analog-to-digital converter
  • the cosine signal is input to ADC 316 to obtain a digitized signal V cos and input to digital signal processing 318.
  • Digital signal processing 318 can include a microprocessor, memory (both volatile and nonvolatile), and support circuitry sufficient to perform the functions as described here. Digital signal processing 318 receives the digitized signal V sin from ADC 314 and the digitized signal V cos from ADC 316 and determines the position of target 116, for example by an arctangent conversion as described above. The calculated position is then available at the output of the digital signal processor 322 in the form of digital data.
  • digital signal processor 322 also determines the type and magnitude of the errors in the received signals V sin and V cos by analyzing characteristic patterns plotted over a period of the rotation. Depending on the type of error (offset, gain, or phase error) the magnitude and error curves, plotted over the full phase, show characteristic patterns, which allows a conclusion of the error type and the magnitude of the error from analysis of the magnitude over the angle pattern. While offset related errors lead to a 1-periodic error signal and a 1-periodic magnitude over one mechanical phase, gain and phase related errors lead to a 2-periodic error signal.
  • a major requirement in a sensor system such as sensor system 100 is the need for understanding the overall error of the sensor information provided by the signal chain in the sensor module (sensor raw data ⁇ analog signal processing ⁇ digital signal processing).
  • An effective way to investigate the error of a sensor system is to compare the sensor results with a known good reference. However, for cost and handling reasons, this method is used only for product development and during end of line calibration in a production line, but is not used on every unit during normal operation.
  • Another effective way is to use a redundant method, where two independent sensors are measuring the same physical parameter (e.g. rotary position) and the Electric Control Unit (ECU) compares the two sensor results. A deviation of the two sensor output signals is considered a failure of the system, but it might not reveal which sensor is defective and which one is operating correctly.
  • ECU Electric Control Unit
  • the sensor signal cannot be interrupted during operation, therefore it is not allowed for example to replace the sensor raw signal with a known reference signal for making a reference measurement. Therefore, the error analysis must be performed with the un-interrupted sine and cosine signals.
  • FIG 4A illustrates an example process 400 that can be executed on digital signal processing 318 as illustrated in Figure 3 .
  • Process 400 receives the sine signal V sin and the cosine signal V cos in step 402. This occurs as shaft 114 is rotated such that target 116 is rotated over receiver coils 106. On each rotation of shaft 114, a number of data points will be received, depending on the relationship between the rotational frequency of shaft 114 and the internal operating clock that determines data sampling of digital signal processing 318.
  • the data is compiled such that all of the V sin and V cos data over a rotational period of shaft 114, for example data can be compiled over a full rotation period or over a number of full rotational periods to reduce the impact of noise by averaging, are stored. This compiled data can be continuously updated on each rotation of shaft 114, or can be updated every few rotations of the shaft.
  • step 406 the error pattern is determined from the compiled V sin and V cos .
  • step 408 the offset, amplitude, and phase parameters are determined based on the error pattern recognition and the magnitude of the errors determined. Steps 406 and 408 are further discussed below in further detail.
  • step 410 corrections to the sine signal V sin and the cosine signal V cos can be determined. These corrections can be input to step 412. Step 412 receives the originally received sine signal V sin and cosine signal V cos and corrects these signals according to the corrections determined by step 410 to provide step 414 with corrected signals V sin and V cos . In step 414, the position of target 116 over receiver coils 106 is determined.
  • the loop that includes steps 412 and 414 can be executed on each sampling cycle of the sine signal V sin and the cosine signal V cos . Therefore, the position determination is accomplished on each sampled values V sin and V cos .
  • the loop of process 400 that includes steps 404 through 410 can be executed on each rotational period of shaft 114 (i.e., through each rotation through 360°) or on selected rotational periods of shaft 114.
  • steps 406, 408, and 410 can be performed with a simple method that allows precise error determination from the sine and cosine signals V sin and V cos without the need of a reference sensor and likewise without the need of a second, redundant sensor.
  • Some methods according to these embodiments are based on the observation that in a sensor system 100 having offset errors, either on one or on both sensor signals (sine and/or cosine), there is a fixed relation between the normalized ripple on the magnitude of the signals and the normalized, full scale peak-to-peak error over a full period of rotation.
  • a sensor system 100 having gain and/or phase errors in the sensor signals (sine and/or cosine) there is the same fixed relation between the normalized ripple on the magnitude of the signal and the normalized peak-to-peak error over a full period.
  • FIG. 4B illustrates a more detailed example of part of process 400, in particular steps 402-410 illustrated in Figure 4B .
  • step 402 the sine signal V sin ( ⁇ ) and the cosine signal V cos ( ⁇ ) are received in digital signal processing 318.
  • Data is then compiled over one or more rotational periods (rotations of ⁇ through 360°) are accumulated in step 404.
  • all of the data points of V sin ( ⁇ ) and V cos ( ⁇ ) can be compiled and stored, in some embodiments data is extracted from the input signals V sin ( ⁇ ) and V cos ( ⁇ ) and stored instead.
  • compilation step 404 can simultaneously compile multiple derived data over the rotational period or periods of the data acquisition.
  • the signals V sin ( ⁇ ) and V cos ( ⁇ ) can be monitored and stored.
  • the minimum and maximum values can be recorded over the rotational period or periods of the data acquisition in step 418.
  • the magnitude is recorded as a function of angle MAG( ⁇ ).
  • step 422 the maximum and minimum values of MAG( ⁇ ) over the data acquisition period can be recorded.
  • step 404 some other values can be calculated and recorded for later use as well.
  • an estimated error can be calculated from the maximum and minimum values of MAG( ⁇ ).
  • MAG norm is determined by determining the minimum MAG( ⁇ ), MAG min , and the maximum MAG( ⁇ ), MAG max , over a full period of compiled data from step 416 and calculating the normalized magnitude ripple MAG norm as discussed above.
  • a normalized error can be estimated from the MAG norm .
  • error case 1.1 illustrates a positive offset error on the sine signal, such as that illustrated in Figures 5A, 5B, and 5C .
  • Error case 1.2 illustrates a negative offset on the sine signal, such as that illustrated in Figures 6A, 6B, and 6C .
  • Error case 1.3 illustrates a positive offset on the cosine signal, such as that illustrated in Figures 7A, 7B, and 7C .
  • Error case 1.4 illustrates a negative offset on the cosine signal such as that illustrated in Figures 8A, 8B, and 8C .
  • Error case 1.5 illustrates a combination of offsets on the sine signal and the cosine signal as is illustrated in Figures 9A, 9B, and 9C .
  • these offset errors illustrate patterns of MAG( ⁇ ) and err( ⁇ ) that are sinusoidal and repeat every period of rotation (1-periodic sinusoidal).
  • the error pattern description and magnitude pattern description columns indicate the positional angle where the maximum and minimum values of err( ⁇ ) and MAG( ⁇ ) are found in the pattern.
  • the last column provides the ratio of the magnitude ripple MAG norm and normalized error err norm .
  • Error cases 2.1, 2.2, 3.1, 3.2, and 3.3 illustrate error cases where the patterns of MAG( ⁇ ) and err( ⁇ ) repeats twice every rotational period (2-periodic sinusoidal) (i.e., there are two maximum values and two minimum values of MAG( ⁇ ) and err( ⁇ ) for each rotational period).
  • Error case 2.1 illustrates a case where the sine signal amplitude is greater than that of the cosine signal, which is illustrated in Figures 10A, 10B, and 10C .
  • Error case 2.2 illustrates a case where the amplitude of the cosine signal is greater than that of the sine signal, which is illustrated in Figures 11A, 11B, and 11C .
  • Error case 3.1 illustrates a case where the cosine signal phase shift from the sine signal is greater than 90°, which is illustrated in Figures 12A, 12B, and 12C .
  • Error case 3.2 illustrates a case where the cosine signal phase shift from the sine signal is less than 90°, which is illustrated in Figures 13A, 13B, and 13C .
  • Error cases 4.1, 4.2, and 4.3 illustrate combinations of 1-periodic and 2-periodic patterned errors.
  • Case 4.1 illustrates a combination of offset and gain errors, which is illustrated in Figures 15A, 15B, and 15C .
  • Case 4.2 illustrates a combination of offset and phase errors, which is illustrated in Figures 16A, 16B, and 16C .
  • Case 4.3 illustrates a combination of offset, gain, and phase errors, which is illustrated in Figures 17A, 17B, and 17C .
  • this ratio of 3.14:1 is maintained only if the type or error is either 1-periodic (from offset errors) or 2-periodic (from gain or phase errors). Combinations of 1-periodic (offset) and 2-periodic (gain or phase) errors lead to non-sinusoidal magnitude and error patterns where there is no fixed ratio between magnitude ripple and maximum error. The ratio will be in a similar region (depending on the type of error), but not exactly 3.14:1. Therefore, in such cases, the magnitude ripple can still be used to determine the error over a full turn, but with less precision.
  • This method also requires that the investigated sensor system is physically rotated by at least a movement that provides half of an electrical period. In practice, especially in constantly rotating systems, a full electrical period will be used as it simplifies the data collection to picking the maximum and minimum magnitude level.
  • the calculated error determined in step 424 as described above is the maximum peak-to-peak error within one electrical period, it cannot be used to calculate the error at a given static position.
  • the error pattern resembles the 1 st derivative of the magnitude waveform, the error at any position can be calculated from the 1 st derivate of the magnitude signal. This could be performed by monitoring not only the maximum and minimum values of the magnitude but also by constantly measuring the magnitude level and calculating the rate of change through the delta of the magnitude over a given change of position in a moving system.
  • the analysis of the sine and cosine signals in a rotating position sensor system also provides inputs that allow an elimination of offset, amplitude mismatch, and phase errors.
  • steps 420, 422, and 424 may be omitted so that the magnitude and error are not calculated using the uncorrected input data V sin ( ⁇ ) and V cos ( ⁇ ). Instead, these calculations may be performed using corrected data so that the resulting error reflects the remaining error after corrections are made, as suggested in steps 442-446 discussed below.
  • the offset errors can be determined.
  • V sin ( ⁇ ) and V cos ( ⁇ ) the peak levels of each signals are recorded and analyzed as discussed above in step 420.
  • Offset COS VCOS max + VCOS min 2 ⁇ V REF
  • Offset SIN is the offset on the sine signal V sin ( ⁇ )
  • Offset COS is the offset on the cosine signal V cos ( ⁇ )
  • VSIN max is the maximum signal level of the sine signal V sin ( ⁇ ) over a full period of rotational motion
  • VSIN min is the minimum signal level of the sine signal V sin ( ⁇ ) over a full period of rotational motion
  • VCOS max is the maximum signal level of the cosine signal V cos ( ⁇ ) over a full period of rotational motion
  • VCOS min is the minimum signal level of the cosine signal V cos ( ⁇ ) over a full period of rotational motion
  • VREF is a reference bias point of the sine and cosine signals.
  • step 428 the calculated Offset SIN can be subtracted from the sine signal V sin ( ⁇ ) to obtain an offset-free sine signal.
  • the calculated Offset COS can be subtracted from the cosine signal V cos ( ⁇ ) to obtain an offset-free cosine signal.
  • the corrected values of V sin ( ⁇ ) and V cos ( ⁇ ) can replace the values recorded in step 416. Consequently, the values of Offset SIN and Offset COS can be provided to step 412 to use to correct the sine and cosine signals during operation.
  • step 430 the amplitude mismatch can be determined.
  • the Amplitude_mismatch is the mismatch of sine and cosine signal levels where a value of 1 represents an ideal matching, VSINmax is the maximum signal level of the sine signal V sin ( ⁇ ), VSINmin is the minimum signal level of the sine signal V sin ( ⁇ ), VCOSmax is the maximum signal level of the cosine signal V cos ( ⁇ ), and VCOSmin is the minimum signal level of the cosine signal V cos ( ⁇ ).
  • V cos ( ⁇ ) By multiplying V cos ( ⁇ ) by the calculated Amplitude_mismatch value, both the sine signals and the cosine signals will have the same amplitude levels. Note that the amplitude correction can be performed whether or not new minimum and maximum values are corrected based on the offset-corrected sine and cosine values.
  • the signals V sin ( ⁇ ) and V cos ( ⁇ ) can be corrected by multiplying the cosine signal V cos ( ⁇ ) by the Amplitude_mismatch.
  • the recorded values of V sin ( ⁇ ) and V cos ( ⁇ ) can be replaced. At this point, the recorded values of V sin ( ⁇ ) and V cos ( ⁇ ) have been corrected for offset and for amplitude mismatch.
  • step 434 through 438 the phase correction is determined.
  • an ideal phase shift of 90° between sine and cosine signals is indicated by one signal crossing the vertical zero line while the opposite signal has either a minimum or a maximum at this position.
  • V sin ( ⁇ ) and V cos ( ⁇ ) the zero-signal crossings no longer occur at one of the peaks of the opposite signal.
  • a simple method to correct phase errors has been described in patent application publication US20130268234A1 "Method and device for determining the absolute position of a movable body," by a co-author if this application.
  • an initial phase shift error between the sine and cosine signals is represented as an amplitude mismatch of the sum and difference signals, which in a subsequent step can be corrected by the same method described for amplitude mismatch correction, or a phase correction can be determined.
  • the sum and difference signals can be determined based on the corrected values of V sin ( ⁇ ) and V cos ( ⁇ ).
  • the value of Sum( ⁇ ) can be calculated as V sin ( ⁇ )+ V cos ( ⁇ ).
  • the value of Diff( ⁇ ) can be determined as V sin ( ⁇ )- V cos ( ⁇ ).
  • both of the signals V sin ( ⁇ ) and V cos ( ⁇ ) have the same amplitude, but a phase relation different from 90°, this phase differences results in an amplitude mismatch between the sum and difference signals.
  • This amplitude mismatch can easily be compensated by measuring the extremes of both signals (sum and difference) to obtain Sum max , Sum min , Diff max , and Diff min and adjusting the amplitudes as discussed above with respect to the amplitude adjustment.
  • step 434 the system proceeds to step 440 where the sum and difference values are then sued to calculate the angular position of target 116.
  • step 434 proceeds to step 436, where the maximum and minimum values of Sum( ⁇ ) and Diff( ⁇ ), Sum max , Sum min , Diff mix . and Diff min can be normalized.
  • Sum norm is the normalized sum values
  • Sum max is the maximum sum value as determined in step 418
  • Sum min is the minimum sum value as determined in step 418
  • Diff norm is the normalized difference value
  • Diff max is the maximum difference value as determined in step 418
  • Diff min is the minimum difference value as determined in step 434.
  • step 438 the sine and cosine signals can be corrected for phase differences based on the phase difference calculated in step 436.
  • the angular position can be calculated using the corrected values of V sin ( ⁇ ) and V cos ( ⁇ ) as described above, these values being corrected for the offset values Offset sin and Offset cos , the amplitude mismatch, and the phase difference ⁇ .
  • step 440 uses the amplitude adjusted sum and difference values that uses V sin ( ⁇ ) and V cos ( ⁇ ) that have been corrected for the offset values Offset sin and Offset cos and the amplitude mismatch to directly calculate the position of target 116.
  • these correction parameters can be updated to step 412, for continuous correction of the sine and cosine signals to provide a rotational position in step 414.
  • the offset correction values, amplitude correction values, and phase correction can be updated while in other embodiments the offset correction values, amplitude correction values, and Sum/Diff amplitude correction values can be uploaded.
  • the remaining angular position error can be calculated.
  • the values of MAG( ⁇ ) can be calculated using the corrected values of V sin ( ⁇ ) and V cos ( ⁇ ) as discussed above.
  • the first derivative of the corrected MAG signal can then be determined.
  • the first derivative of MAG( ⁇ ) can be determined by monitoring its change as a function of positional angle through a particular range of positional angles.
  • the first derivative of MAG( ⁇ ) is indicative of the shape of the error err( ⁇ ) and the peak-peak value of err( ⁇ ) is related to the magnitude ripple value as discussed above.
  • the MAG signals stored in step 420 can be calculated The magnitude pattern and the first derivative with respect to angular position over a half or full period can be analyzed to determine the remaining error as described above.
  • a dynamic signal correction may consist of the following actions.
  • the method steps as described in Figures 4A and 4B may occur in any order, and may be executing simultaneously. Therefore, embodiments of the present invention can include (1) constantly monitor sine and cosine input signals while the position sensor system is rotating as described in step 404; (2) Record the minimum and maximum levels of the sine and cosine signals as described in step 416; (3) Determine the correct offset errors as described above with respect to step 426; (4) Apply offset correction to both sine and cosine signals as illustrated in step 428; (5) Correct amplitude mismatch as described above in step 430; (6) Apply the amplitude mismatch correction as described in step 432; (7) Apply phase correction described above, which includes calculating sum and difference of sine and cosine signals as described in step 418 and using amplitude adjusted sum and difference values to directly calculate the position or by normalizing the sum and difference values to calculate the phase difference as described in step 436 and 438; (8) Calculate
  • the correction of the sine and cosine signals and the calculation of the angular position can be performed throughout the process or, as illustrated in Figure 4A , as a separate step.
  • sine and cosine data that has been corrected for offsets and amplitude variation can be used.
  • the sine and cosine data itself is recorded in step 404 and the sum and difference signals are calculated during step 434.
  • Calculation of the correction values as described in Figures 4A and 4B can be performed continuously while system 100 is operating. Alternatively, the process described in Figures 4A and 4B can be performed periodically and the correction parameters updated accordingly. In steps 412 and 414, the latest updated correction parameters can then be used to continuously correct the values of V sin ( ⁇ ) and V cos ( ⁇ ) received in digital signal processing 318.
  • Figures 5A, 5B, and 5C illustrate an example with a positive offset on V sin ( ⁇ ) with no corresponding offset on V cos ( ⁇ ), which corresponds to case 1.1 of Table 1.
  • Figure 5A illustrates plots of V sin ( ⁇ ) and V cos ( ⁇ ) along with the corresponding values of MAG( ⁇ ) and the error err( ⁇ ).
  • Figure 5B is a plot of the values of MAG( ⁇ ) and err( ⁇ ) under the circumstance illustrated in
  • Figure 5A Figure 5C illustrates a polar graph of MAG( ⁇ ) overlaid on an ideal polar plot of magnitude for comparison.
  • an offset on the sine signal V sin ( ⁇ ) results in a 1-periodic pattern in MAG( ⁇ ) and err( ⁇ ).
  • This example illustrates a 5% positive offset on the sine signal V sin ( ⁇ ).
  • the pattern of err( ⁇ ) is phase shifted by 90 electrical degrees (1st derivative) relative to the pattern of MAG( ⁇ ).
  • the positive maximum of err( ⁇ ) (err max ) occurs at a position of 0° while the negative maximum (err min ) occurs at 180°.
  • the positive maximum of MAG( ⁇ ) occurs at a position of 90° while the negative maximum (MAG min ) occurs at 270°.
  • the ratio between normalized magnitude ripple and peak-to-peak normalized error is fixed at a ratio of 3.14 : 1, based on the normalized magnitude ripple MAG norm and the peak-to-peak normalized error err norm as discussed above.
  • the polar plot illustrated in Figure 5C shows the ideal figure as dotted circle compared with MAG( ⁇ ), the actual pattern is shifted up on the Y-axis, the sine axis.
  • Figures 6A, 6B, and 6C illustrate an example with a negative offset on V sin ( ⁇ ) with no corresponding offset on V cos ( ⁇ ), which corresponds to error case 1.2 in Table 1.
  • Figure 6A illustrates plots of V sin ( ⁇ ) and V cos ( ⁇ ) along with the corresponding values of MAG( ⁇ ) and the error err( ⁇ ).
  • Figure 6B is a plot of the values of MAG( ⁇ ) and err( ⁇ ) under the circumstances illustrated in Figure 6A.
  • Figure 6C illustrates a polar graph of MAG( ⁇ ) overlaid on an ideal polar plot of magnitude for comparison.
  • Figures 6A, 6B, and 6C illustrate a negative offset on the sine signal V sin ( ⁇ ) results in a 1-periodic pattern in MAG( ⁇ ) and err( ⁇ ).
  • This example illustrates a 5% negative offset on the sine signal V sin ( ⁇ ).
  • the pattern of err( ⁇ ) is phase shifted by 90 electrical degrees (1st derivative) relative to the pattern of MAG( ⁇ ).
  • the positive maximum of err( ⁇ ) (err max ) occurs at a position of 180° while the negative maximum (err min ) occurs at 0°.
  • the positive maximum of MAG( ⁇ ) (MAG max ) occurs at a position of 270° while the negative maximum (MAG min ) occurs at 90°.
  • Normalized magnitude ripple and peak-to-peak normalized error is fixed at a ratio of 3.14 : 1, based on the normalized magnitude ripple MAG norm and the peak-to-peak normalized error err norm as discussed above.
  • the polar plot illustrated in Figure 6C shows the ideal figure as dotted circle, the actual pattern MAG( ⁇ ) is shifted down on the Y-axis (sine).
  • Figures 7A, 7B, and 7C illustrate an example with a positive offset on V cos ( ⁇ ) with no corresponding offset on V sin ( ⁇ ), which corresponds to error case 1.3 in Table 1.
  • Figure 7A illustrates plots of V sin ( ⁇ ) and V cos ( ⁇ ) along with the corresponding values of MAG( ⁇ ) and the error err( ⁇ ).
  • Figure 7B is a plot of the values of MAG( ⁇ ) and err( ⁇ ) under the circumstances illustrated in Figure 7A.
  • Figure 7C illustrates a polar graph of MAG( ⁇ ) overlaid on an ideal polar plot of magnitude for comparison.
  • Figures 7A, 7B, and 7C illustrate the effects of the positive offset on a cosine signal.
  • FIG. 7A, 7B, and 7C illustrate an example having a 5% positive offset on the cosine signal V cos ( ⁇ ).
  • the pattern in error err( ⁇ ) is phase shifted by 90 electrical degrees (1st derivative) relative to the pattern in MAG( ⁇ ).
  • the positive maximum of err( ⁇ ) (err max ) occurs at a position of 270° while the negative maximum (err min ) occurs at 90°.
  • the positive maximum of MAG( ⁇ ) (MAG max ) occurs at a position of 0° while the negative maximum (MAG min ) occurs at 180°.
  • Normalized magnitude ripple and peak-to-peak normalized error is fixed at a ratio of 3.14 : 1, based on the normalized magnitude ripple MAG norm and the peak-to-peak normalized error err norm as discussed above.
  • the polar plot of Figure 7C shows the ideal figure as a dotted circle along with the actual pattern of MAG( ⁇ ), which as illustrated is shifted right on the X-axis (cosine).
  • Figures 8A, 8B, and 8C illustrate an example with a negative offset on V cos ( ⁇ ) with no corresponding offset on V sin ( ⁇ ), which corresponds to error case 1.4 of Table 1.
  • Figure 8A illustrates plots of V sin ( ⁇ ) and V cos ( ⁇ ) along with the corresponding values of MAG( ⁇ ) and the error err( ⁇ ).
  • Figure 8B is a plot of the values of MAG( ⁇ ) and err( ⁇ ) under the circumstances illustrated in Figure 8A.
  • Figure 8C illustrates a polar graph of MAG( ⁇ ) overlaid on an ideal polar plot of magnitude for comparison.
  • Figures 8A, 8B, and 8C illustrate a negative offset on cosine signal, which results in a 1-periodic pattern in MAG( ⁇ ) and err( ⁇ ).
  • Figures 8A, 8B, and 8C illustrate an example having a 5% negative offset on the cosine signal V cos ( ⁇ ).
  • the pattern of err( ⁇ ) is phase shifted by 90 electrical degrees (1st derivative) relative to the pattern of Magnitude MAG( ⁇ ). As is illustrated, the positive maximum of err( ⁇ ) (err max ) occurs at a position of 90° while the negative maximum (err min ) occurs at 270°.
  • MAG max positive maximum of MAG( ⁇ )
  • MAG min negative maximum
  • Normalized magnitude ripple and peak-to-peak normalized error is fixed at a ratio of 3.14 : 1, based on the normalized magnitude ripple MAG norm and the peak-to-peak normalized error err norm as discussed above.
  • the polar plot illustrated in Figure 8C shows the ideal figure as dotted circle overlaid on the actual pattern of MAG( ⁇ ), which is shifted left on the X-axis (cosine).
  • Figures 9A, 9B, and 9C illustrate an example with a combination of offsets on both the cosine signal V cos ( ⁇ ) and the sine signal V sin ( ⁇ ), which corresponds to error case 1.5 in Table 1.
  • Figure 9A illustrates plots of V sin ( ⁇ ) and V cos ( ⁇ ) along with the corresponding values of MAG( ⁇ ) and the error err( ⁇ ).
  • Figure 9B is a plot of the values of MAG( ⁇ ) and err( ⁇ ) under the circumstances illustrated in Figure 9A.
  • Figure 9C illustrates a polar graph of MAG( ⁇ ) overlaid on an ideal polar plot of magnitude for comparison.
  • Figures 9A, 9B, and 9C illustrate a combination of offsets on both the sine and cosine signals V cos ( ⁇ ) and V sin ( ⁇ ), which results in a 1-periodic pattern in both Magnitude MAG( ⁇ ) and error err( ⁇ ).
  • Figures 9A, 9B, and 9C illustrate an example having a 5% positive offset on the sine signal V sin ( ⁇ ) and a 5% negative offset on the cosine signal V cos ( ⁇ ).
  • the pattern in error err( ⁇ ) is phase shifted by 90 electrical degrees (1st derivative) relative to the pattern in magnitude MAG( ⁇ ).
  • the positive maximum of err( ⁇ ) (err max ) and negative maximum (err min ) occurs at variable locations, but are characterized with a 1-periodic sinusoidal pattern.
  • the positive maximum of MAG( ⁇ ) (MAG max ) and the negative maximum (MAG min ) are variable, but are characterized with a 1-periodic sinusoidal pattern that is shifted in position by 90° from that of the error maxima.
  • Magnitude ripple and peak-to-peak normalized error is fixed at a ratio of 3.14 : 1, based on the normalized magnitude ripple MAG norm and the peak-to-peak normalized error err norm as discussed above.
  • the polar plot illustrated in Figure 9C shows the ideal figure as dotted circle the actual pattern of MAG( ⁇ ), which is shifted both left on the X-axis (cosine) and up on the Y-axis (sine).
  • Figures 10A, 10B, and 10C illustrate an example where the amplitude of the cosine signal V cos ( ⁇ ) is less than that of the sine signal V sin ( ⁇ ), which corresponds to error case 2.1 of Table 1.
  • Figure 10A illustrates plots of V sin ( ⁇ ) and V cos ( ⁇ ) along with the corresponding values of MAG( ⁇ ) and the error err( ⁇ ).
  • Figure 10B is a plot of the values of magnitude MAG( ⁇ ) and error err( ⁇ ) under the circumstances illustrated in Figure 10A.
  • Figure 10C illustrates a polar graph of MAG( ⁇ ) overlaid on an ideal polar plot of magnitude for comparison.
  • Figures 10A, 10B, and 10C illustrate an amplitude of the sine signal V sin ( ⁇ ) that is greater than the amplitude of the cosine signal V cos ( ⁇ ).
  • FIG. 10A, 10B, and 10C illustrate an example having a 5% larger sine signal V sin ( ⁇ ) relative to the cosine signal V cos ( ⁇ ).
  • the pattern in error err( ⁇ ) is phase shifted by 90 electrical degrees (1st derivative) relative to the pattern in magnitude MAG( ⁇ ).
  • the positive maximum of err( ⁇ ) (err max ) occurs at a positions 45° and 225° while the negative maximum (err min ) occurs at 135° and 315°.
  • MAG max the positive maximum of MAG( ⁇ )
  • MAG min the negative maximum
  • Magnitude ripple and peak-to-peak normalized error is fixed at a ratio of 3.14 : 1, based on the normalized magnitude ripple MAG norm and the peak-to-peak normalized error err norm as discussed above.
  • the polar plot illustrated in Figure 10C shows the ideal figure as dotted circle and the actual pattern MAG( ⁇ ) in this example, which is stretched in the Y-axis (sine).
  • Figures 11A, 11B, and 11C illustrate an example where the amplitude of the cosine signal V cos ( ⁇ ) is greater than that of the sine signal V sin ( ⁇ ), which corresponds to error case 2.2 of Table 1.
  • Figure 11A illustrates plots of V sin ( ⁇ ) and V cos ( ⁇ ) along with the corresponding values of MAG( ⁇ ) and the error err( ⁇ ).
  • Figure 11B is a plot of the values of magnitude MAG( ⁇ ) and error err( ⁇ ) under the circumstances illustrated in Figure 11A.
  • Figure 11C illustrates a polar graph of MAG( ⁇ ) overlaid on an ideal polar plot of magnitude for comparison for the example illustrated in Figure 11A.
  • Figures 11A, 11B, and 11C illustrate an example where the amplitude of the cosine signal V cos ( ⁇ ) is greater than the amplitude of the sine signal V sin ( ⁇ ).
  • An amplitude mismatch between the sine and cosine signals V sin ( ⁇ ) and V cos ( ⁇ ) results in a 2-periodic pattern in magnitude MAG( ⁇ ) and error err( ⁇ ).
  • Figures 11A, 11B, and 11C show an example having a 5% larger cosine signal V cos ( ⁇ ) relative to the sine signal V sin ( ⁇ ).
  • the pattern of error err( ⁇ ) is phase shifted by 90 electrical degrees (1st derivative) relative to the pattern of the magnitude MAG( ⁇ ).
  • the positive maximum of err( ⁇ ) occurs at a positions 135° and 315° while the negative maximum (err min ) occurs at 45° and 225°.
  • the positive maximum of MAG( ⁇ ) occurs at a position of 0° and 180° while the negative maximum (MAG min ) occurs at 90° and 270°.
  • Magnitude ripple and peak-to-peak normalized error is fixed at a ratio of 3.14 : 1, based on the normalized magnitude ripple MAG norm and the peak-to-peak normalized error err norm as discussed above.
  • the polar plot illustrated in Figure 11C shows the ideal figure as dotted circle with the actual pattern of MAG( ⁇ ), which is stretched in the X-axis (cosine).
  • Figures 12A, 12B, and 12C illustrate an example where cosine signal V cos ( ⁇ ) to sine phase signal V sin ( ⁇ ) is less than 90 degrees, which corresponds to error case 3.1 of Table 1.
  • Figure 12A illustrates plots of V sin ( ⁇ ) and V cos ( ⁇ ) along with the corresponding values of MAG( ⁇ ) and the error err( ⁇ ).
  • Figure 12B is a plot of the values of magnitude MAG( ⁇ ) and error err( ⁇ ) under the circumstances illustrated in Figure 12A.
  • Figure 12C illustrates a polar graph of MAG( ⁇ ) overlaid on an ideal polar plot of magnitude for comparison for the example illustrated in Figure 12A .
  • Figures 12A, 12B, and 12C illustrate a cosine to sine phase shift of less than 90 degrees.
  • a phase mismatch between sine and cosine V sin ( ⁇ ) and V cos ( ⁇ ) signals of ⁇ 90° results in a 2-periodic pattern in magnitude MAG( ⁇ ) and error err( ⁇ ).
  • the pattern of error err( ⁇ ) is phase shifted by 90 electrical degrees (1st derivative) relative to the pattern of magnitude MAG( ⁇ ).
  • the positive maximum of err( ⁇ ) occurs at a positions 0° and 180° while the negative maximum (err min ) occurs at 90° and 270°.
  • the positive maximum of MAG( ⁇ ) occurs at a position of 45° and 225° while the negative maximum (MAG min ) occurs at 135° and 315°.
  • Magnitude ripple and peak-to-peak normalized error is fixed at a ratio of 3.14 : 1, based on the normalized magnitude ripple MAG norm and the peak-to-peak normalized error err norm as discussed above. but the absolute error is always negative.
  • the polar plot illustrated in Figure 12C shows the ideal figure as dotted circle and the actual pattern of MAG( ⁇ ), which is stretched in the 45° direction.
  • Figures 13A, 13B, and 13C illustrate an example where cosine signal V cos ( ⁇ ) to sine phase signal V sin ( ⁇ ) is greater than 90 degrees, which corresponds to error case 3.2 of Table 1.
  • Figure 13A illustrates plots of V sin ( ⁇ ) and V cos ( ⁇ ) along with the corresponding values of MAG( ⁇ ) and the error err( ⁇ ).
  • Figure 13B is a plot of the values of magnitude MAG( ⁇ ) and error err( ⁇ ) under the circumstances illustrated in Figure 13A.
  • Figure 13C illustrates a polar graph of MAG( ⁇ ) overlaid on an ideal polar plot of magnitude MAG( ⁇ ) for comparison in the example illustrated in Figure 13A.
  • Figures 13A, 13B, and 13C illustrate a cosine to sine phase shift of greater than 90 degrees.
  • FIG. 13A, 13B, and 13C show an example having a 95° phase shift of the cosine signal relative to the sine signal (i.e. the phase shift discussed above ⁇ is 5°).
  • the pattern in err( ⁇ ) is phase shifted by 90 electrical degrees (1st derivative) relative to the pattern in magnitude MAG( ⁇ ).
  • the positive maximum of err( ⁇ ) (err max ) occurs at a positions 90° and 270° while the negative maximum (err min ) occurs at 0° and 180°.
  • Figures 14A, 14B, and 14C illustrate an example with a combination of gain and phase errors in the cosine signal V cos ( ⁇ ) and the sine signal V sin ( ⁇ ), which corresponds to case 3.3 of Table 1.
  • Figure 14A illustrates plots of V sin ( ⁇ ) and V cos ( ⁇ ) along with the corresponding values of MAG( ⁇ ) and the error err( ⁇ ).
  • Figure 14B is a plot of the values of magnitude MAG( ⁇ ) and error err( ⁇ ) under the circumstances illustrated in Figure 14A.
  • Figure 14C illustrates a polar graph of MAG( ⁇ ) overlaid on an ideal polar plot of magnitude MAG( ⁇ ) for comparison in the example illustrated in Figure 14A.
  • Figures 14A, 14B, and 14C illustrate a combination of gain and phase errors. The combination of both amplitude and phase mismatch between sine and cosine signals
  • V sin ( ⁇ ) and V cos ( ⁇ ) results in a 2-periodic pattern in magnitude MAG( ⁇ ) and error err( ⁇ ).
  • Figures 14A, 14B, and 14C illustrate an example having a 93° phase shift of the cosine signal V cos ( ⁇ ) relative to the sine signal V sin ( ⁇ ) and a sine signal V sin ( ⁇ ) that is 5% larger relative to the cosine signal V cos ( ⁇ ).
  • the pattern for err( ⁇ ) is phase shifted by 90 electrical degrees (1st derivative) relative to the pattern of magnitude MAG( ⁇ ).
  • the positive maximum of err( ⁇ ) (err max ) and the negative maximum (err min ) occur at variable locations.
  • Magnitude ripple and peak-to-peak normalized error is fixed at a ratio of 3.14 : 1, based on the normalized magnitude ripple MAG norm and the peak-to-peak normalized error err norm as discussed above. However, the error is not symmetric to zero.
  • the polar plot illustrated in Figure 14C shows the ideal figure as dotted circle and the actual pattern of magnitude MAG( ⁇ ), which is stretched in both the X-axis and in 135° direction.
  • Figures 15A, 15B, and 15C illustrate an example with a combination of offset and gain errors in the cosine signal V cos ( ⁇ ) and the sine signal V sin ( ⁇ ), which corresponds to error case 4.1 of Table 1.
  • Figure 15A illustrates plots of V sin ( ⁇ ) and V cos ( ⁇ ) along with the corresponding values of MAG( ⁇ ) and the error err( ⁇ ).
  • Figure 15B is a plot of the values of magnitude MAG( ⁇ ) and error err( ⁇ ) under the circumstances illustrated in Figure 15A.
  • Figure 15C illustrates a polar graph of MAG( ⁇ ) overlaid on an ideal polar plot of magnitude MAG( ⁇ ) for comparison in the example illustrated in Figure 15A.
  • Figures 15A, 15B, and 15C illustrate a combination of offset and gain errors.
  • the combination of both offset errors and amplitude mismatch between sine and cosine signals V sin ( ⁇ ) and V cos ( ⁇ ) results in a non- sinusoidal pattern in magnitude MAG( ⁇ ) and error err( ⁇ ), combining both 1-periodic and 2-periodic elements.
  • Figures 15A, 15B, and 15C show an example having a 3% offset and 5% gain mismatch of the cosine signal V cos ( ⁇ ) relative to the sine signal V sin ( ⁇ ).
  • the pattern in error err( ⁇ ) does not resemble a sinusoidal waveform and is also no longer the direct 1st derivative of the pattern in magnitude MAG( ⁇ ).
  • the ratio between the ripple in magnitude MAG( ⁇ ) and the peak-to-peak in error err( ⁇ ) is not fixed at 3.14 : 1. In this particular case, the ratio is 2.75:1.
  • the polar plot illustrated in Figure 15C shows the ideal figure as dotted circle and the actual pattern of magnitude MAG( ⁇ ), which is stretched and/or shifted in any direction depending on the signal having an offset and the amplitude mismatch (sine > cosine or cosine > sine). There is still a resemblance between the normalized magnitude ripple and peak-to-peak error, but since this ratio is no longer fixed at 3.14:1, the error estimation for such multi-point failures can only be made with less precision.
  • Figures 16A, 16B, and 16C illustrate an example with a combination of offset and phase errors in the cosine signal V cos ( ⁇ ) and the sine signal V sin ( ⁇ ), which corresponds to error case 4.2 of Table 1.
  • Figure 16A illustrates plots of V sin ( ⁇ ) and V cos ( ⁇ ) along with the corresponding values of MAG( ⁇ ) and the error err( ⁇ ).
  • Figure 16B is a plot of the values of magnitude MAG( ⁇ ) and error err( ⁇ ) under the circumstances illustrated in Figure 16A.
  • Figure 16C illustrates a polar graph of MAG( ⁇ ) overlaid on an ideal polar plot of magnitude MAG( ⁇ ) for comparison in the example illustrated in Figure 16A.
  • Figures 16A, 16B, and 16C illustrate a combination of offset and phase errors.
  • the combination of both offset and phase errors between sine and cosine signals V sin ( ⁇ ) and V cos ( ⁇ ) results in a non- sinusoidal pattern in magnitude MAG( ⁇ ) and error err( ⁇ ), combining both 1-periodic and 2-periodic elements.
  • Figures 16A, 16B, and 16C show an example having a 5% offset and 95° phase shift of the cosine signal V cos ( ⁇ ) relative to the sine signal V sin ( ⁇ ).
  • the pattern of err( ⁇ ) does not resemble a sinusoidal waveform and is also no longer the direct 1st derivative of the pattern of magnitude MAG( ⁇ ) pattern.
  • the ratio between the normalized magnitude ripple MAG norm and the normalized peak-to-peak in error err norm is not fixed at 3.14 : 1, in this particular case, the ratio is 3.53:1.
  • the polar plot illustrated in Figure 16C shows the ideal figure as dotted circle and the actual pattern MAG( ⁇ ), which is stretched and/or shifted in the 45° or 135° direction depending on the signal having an offset and the type of phase shift (below or above 90°). There is still a resemblance between the ripple of magnitude MAG( ⁇ ) and the peak-to-peak of error err( ⁇ ), but since this ratio is no longer fixed at 3.14:1 the error estimation for such multi-point failures can only be made with less precision.
  • Figures 17A, 17B, and 17C illustrate an example with a combination of offset, gain, and phase errors in the cosine signal V cos ( ⁇ ) and the sine signal V sin ( ⁇ ), which corresponds to error case 4.3 of Table 1.
  • Figure 17A illustrates plots of V sin ( ⁇ ) and V cos ( ⁇ ) along with the corresponding values of MAG( ⁇ ) and the error err( ⁇ ).
  • Figure 17B is a plot of the values of magnitude MAG( ⁇ ) and error err( ⁇ ) under the circumstances illustrated in Figure 17A.
  • Figure 17C illustrates a polar graph of MAG( ⁇ ) overlaid on an ideal polar plot of magnitude MAG( ⁇ ) for comparison in the example illustrated in Figure 17A.
  • Figures 17A, 17B, and 17C illustrate a combination of offset, gain, and phase errors, which results in a non-sinusoidal pattern in magnitude MAG( ⁇ ) and error err( ⁇ ), combining both 1-periodic and 2-periodic elements.
  • Figures 17A, 17B, and 17C show an example having a 3% offset of the sine signal V sin ( ⁇ ), a 5% larger cosine signal V cos ( ⁇ ) relative to the sine signal V sin ( ⁇ ), and an 87° phase shift between the cosine signal V cos ( ⁇ ) and the sine signal V sin ( ⁇ ).
  • the pattern in error err( ⁇ ) does not resemble a sinusoidal waveform and is also no longer the direct 1st derivative of the pattern in magnitude MAG( ⁇ ).
  • the ratio between in the normalized magnitude ripple MAG norm and the normalized peak-to-peak error err norm is not fixed at 3.14 : 1, in this particular case, the ratio is 3.15:1.
  • the polar plot illustrated in Figure 17C shows the ideal figure as dotted circle and the actual pattern of magnitude MAG( ⁇ ), which is both shifted, stretched and rotated, depending on the signal having an offset and gain mismatch and the type of phase shift (below or above 90°). There is still a resemblance between the ripple of magnitude MAG( ⁇ ) and the peak-to-peak in error err( ⁇ ), but since this ratio is no longer fixed at 3.14:1, the error estimation for such multi-point failures can only be made with less precision.
  • the error estimation from the Magnitude ripple provides an error estimation with high precision.
  • the method can also be applied to multi-point failures, as long as the failures result from the same error type, having either 1-periodic or 2-periodic patterns. For multi-point failures which are a combination of 1-periodic and 2-periodic failures, this method can only be applied with less precision.

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Claims (9)

  1. Verfahren zum Korrigieren von Fehlern in einem Drehpositionssensor (100) mit Korrekturparametern, die Versatzkorrekturparameter, Amplitudendifferenzparameter und Phasenkorrekturparameter umfassen, das Folgendes umfasst:
    Empfangen von Sinussignalen und von Kosinussignalen, wobei die Sinussignale und die Kosinussignale eine Funktion einer Motorwelle (114), die sich über Empfängerspulen (106) des Drehpositionssensors (100) dreht, sind;
    Kompilieren und Speichern von Sinusdaten aus den Sinussignalen und von Kosinusdaten aus den Kosinussignalen über eine Drehperiode der Motorwelle (114),
    Bestimmen (426) der Versatzkorrekturparameter aus den Sinusdaten und den Kosinusdaten;
    Korrigieren (428) der Sinusdaten und der Kosinusdaten mit den Versatzkorrekturparametern, um versatzkorrigierte Sinusdaten und Kosinusdaten zu erhalten;
    Bestimmen (430) der Amplitudendifferenzparameter aus den versatzkorrigierten Sinusdaten und Kosinusdaten;
    Korrigieren (432) der versatzkorrigierten Sinusdaten und Kosinusdaten mit den Amplitudendifferenzparametern, um amplitudenkorrigierte Sinusdaten und Kosinusdaten zu erhalten;
    Bestimmen (434-436) der Phasendifferenzparameter aus der Summe und der Differenz der amplitudenkorrigierten Sinusdaten und Kosinusdaten;
    Korrigieren (438) der amplitudenkorrigierten Sinusdaten und Kosinusdaten mit den Phasendifferenzparametern, um phasenfehlerkorrigierte Sinusdaten und Kosinusdaten zu erhalten;
    Verwenden der Versatzkorrekturparameter, der Amplitudendifferenzparameter und der Phasendifferenzparameter, um das Sinussignal und das Kosinussignal zu korrigieren (412);
    Berechnen (442) von Magnitudendaten aus den phasenfehlerkorrigierten Sinusdaten und Kosinusdaten;
    Bestimmen (444) einer ersten Ableitung der Magnitudendaten als eine Funktion der Winkelposition;
    Bestimmen (446) einer verbleibenden Winkelpositionskorrektur aus der ersten Ableitung; und
    Aktualisieren (448) der Korrekturparameter in Übereinstimmung mit der verbleibenden Winkelpositionskorrektur.
  2. Verfahren nach Anspruch 1, wobei das Kompilieren und Speichern von Sinusdaten und Kosinusdaten Folgendes umfasst:
    Aufzeichnen (416) von Werten der Sinussignale und der Kosinussignale über die Periode; und
    Bestimmen (418) der minimalen und maximalen Werte der Sinussignale und der Kosinussignale aus den Werten.
  3. Verfahren nach Anspruch 2, wobei das Kompilieren von Daten ferner Folgendes umfasst:
    Bestimmen (420) von Magnitudendaten aus den Sinussignalen und den Kosinussignalen über die Periode;
    Bestimmen (422) maximaler und minimaler Magnitudendaten; und
    Bestimmen (424) eines geschätzten Fehlers aus dem Maximum und dem Minimum der Magnitudendaten.
  4. Verfahren nach Anspruch 3, wobei das Bestimmen des geschätzten Fehlers Folgendes umfasst:
    Bestimmen einer normierten Magnitude aus der maximalen und der minimalen Magnitude; und
    Bestimmen des geschätzten Fehlers aus der normierten Magnitude.
  5. Verfahren nach Anspruch 1, wobei das Bestimmen der Versatzparameter das Bestimmen eines Sinusversatzes, der durch den Durchschnitt der minimalen und maximalen Sinussignale in den Sinusdaten, die durch eine Referenzspannung eingestellt sind, gegeben ist, und eines Kosinusversatzes, der durch den Durchschnitt der minimalen und maximalen Kosinussignale in den Kosinusdaten, die durch die Referenzspannung eingestellt sind, gegeben ist, umfasst.
  6. Verfahren nach Anspruch 1, wobei das Bestimmen der Amplitudendifferenzparameter das Bestimmen der Differenz zwischen dem maximalen Sinussignal und dem minimalen Sinussignal in den versatzkorrigierten Sinusdaten, dividiert durch die Differenz zwischen dem maximalen Kosinussignal und dem minimalen Kosinussignal in den versatzkorrigierten Kosinusdaten, umfasst.
  7. Verfahren nach Anspruch 1, wobei das Bestimmen der Phasendifferenzparameter Folgendes umfasst:
    Bestimmen des Maximums und des Minimums der Summe der Sinussignale und der Kosinussignale in den amplitudenkorrigierten Sinusdaten und Kosinusdaten über die Periode;
    Bestimmen des Maximums und des Minimums der Differenz des Sinussignals und des Kosinussignals in den amplitudenkorrigierten Sinusdaten und Kosinusdaten über die Periode;
    Bestimmen einer normierten Summe, die durch die Differenz zwischen der maximalen Summe und der minimalen Summe, dividiert durch die Summe der maximalen Summe und der minimalen Summe, gegeben ist;
    Bestimmen einer normierten Differenz, die durch die Differenz zwischen der maximalen Differenz und der minimalen Differenz, dividiert durch die Summe der maximalen Differenz und der minimalen Differenz, gegeben ist; und
    Bestimmen des Phasenwinkels als das Doppelte des Arcustangens des Verhältnisses zwischen der normierten Differenz und der normierten Summe.
  8. Verfahren Anspruch 1, wobei die Versatzkorrekturparameter, die Amplitudendifferenzparameter und die Phasendifferenzparameter periodisch berechnet werden.
  9. Verfahren nach Anspruch 1, wobei die Versatzkorrekturparameter, die Amplitudendifferenzparameter und die Phasendifferenzparameter ununterbrochen berechnet werden.
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